Multiscale Magnetic Underdense Regions on the Solar Surface: Granular and Mesogranular Scales

The Sun is a non-equilibrium, dissipative system subject to an energy flow that originates in its core. Convective overshooting motions create temperature and velocity structures that show a temporal and spatial multiscale evolution. As a result, photospheric structures are generally considered to be a direct manifestation of convective plasma motions. The plasma flows in the photosphere govern the motion of single magnetic elements. These elements are arranged in typical patterns, which are observed as a variety of multiscale magnetic patterns. High-resolution magnetograms of the quiet solar surface revealed the presence of multiscale magnetic underdense regions in the solar photosphere, commonly called voids, which may be considered to be a signature of the underlying convective structure. The analysis of such patterns paves the way for the investigation of all turbulent convective scales, from granular to global. In order to address the question of magnetic structures driven by turbulent convection at granular and mesogranular scales, we used a voids-detection method. The computed distribution of void length scales shows an exponential behavior at scales between 2 and 10 Mm and the absence of features at mesogranular scales. The absence of preferred scales of organization in the 2?–?10 Mm range supports the multiscale nature of flows on the solar surface and the absence of a mesogranular convective scale.     

Specifics of the solar photospheric convection at granulation,mesogranulation, and supergranulation scales

The power spectra of temperature and vertical velocity variations in the solar photosphere are calculated using the data obtained through observations of a nonperturbed region near the solar disk center in the neutral iron line λ ≈ 639.3 nm conducted at the 70 cm German Vacuum Tower Telescope (VTT) located in the Canary Islands (Spain). The variations of these spectra with altitude are analyzed. It is found that the primary power in the lower photosphere is localized in the range of frequencies that correspond to granulation with a peak at the λ ≈ 1.5–2.0 Mm scale and is reduced with altitude, the power spectrum maximum in the upper photospheric layers is shifted towards larger scales (Δλ ≤ 1 Mm), and the power of variations of the vertical supergranulation velocity (λ ≈ 20–30 Mm) virtually does not change with altitude. An isolated mesogranulation regime (λ ≈ 5–12 Mm) is not found at any of the studied altitudes. The obtained results suggest that the convective structure of the solar photosphere at mesogranulation scales behaves like granulation: the mesostructures are a part of an extended distribution of granulation scales. It is shown that the supergranulation flows are stable throughout the entire photosphere and reach much higher altitudes than the granulation flows.     

Horizontal convective velocity field obtained from the observations of the solar limb

Structure of horizontal convective currents in the solar atmosphere has been investigated using profiles of the λ ≈ 532.42 nm neutral iron line which were observed at the solar limb with high spatial resolution. The asymmetry of the observed line was shown to arise when approaching the solar limb. The spatial and time velocity variations were simulated using the λ-meter technique. Acoustic waves were removed using the k-ω filters. The convection currents on various spatial scales were distinguished, namely, those connected with granulation, mesogranulation, and supergranulation. The spatial and time distribution of the convection velocities in the photosphere and in the low chromosphere has been analyzed. The horizontal currents were shown to exist on granulation, mesogranulation, and supergranulation scales as low as h ≈ 250 km, and the granulation and mesogranulation horizontal velocities increase with height. In the photospheric layers, the supergranulation vertical-velocity field appears almost invariable, while the supergranulation horizontal-velocity field can vary with height. The horizontal velocity distribution within large convection currents is found to be asymmetric on granulation, mesogranulation, and supergranulation scales.     

Evolution of the Sun’s Polar Fields and the Poleward Transport of Remnant Magnetic Flux

Observations of the solar photosphere show spatially compact large-amplitude Doppler velocity events with short lifetimes. In data from the Imaging Magnetograph eXperiment (IMaX) on the first flight of the Sunrise balloon in 2009, events with velocities in excess of 4\(\sigma \) from the mean can be identified in both intergranular downflow lanes and granular upflows. We show that the statistics of such events are consistent with the random superposition of strong convective flows and p-mode coherence patches. Such coincident superposition complicates the identification of acoustic wave sources in the solar photosphere, and may be important in the interpretation of spectral line profiles formed in solar photosphere.

     

The Horizontal Component of Photospheric Plasma Flows During the Emergence of Active Regions on the Sun

The dynamics of horizontal plasma flows during the first hours of the emergence of active region magnetic flux in the solar photosphere have been analyzed using SOHO/MDI data. Four active regions emerging near the solar limb have been considered. It has been found that extended regions of Doppler velocities with different signs are formed in the first hours of the magnetic flux emergence in the horizontal velocity field. The flows observed are directly connected with the emerging magnetic flux; they form at the beginning of the emergence of active regions and are present for a few hours. The Doppler velocities of flows observed increase gradually and reach their peak values 4?–?12 hours after the start of the magnetic flux emergence. The peak values of the mean (inside the ±?500 m?s^?1 isolines) and maximum Doppler velocities are 800?–?970 m?s^?1 and 1410?–?1700 m?s^?1, respectively. The Doppler velocities observed substantially exceed the separation velocities of the photospheric magnetic flux outer boundaries. The asymmetry was detected between velocity structures of leading and following polarities. Doppler velocity structures located in a region of leading magnetic polarity are more powerful and exist longer than those in regions of following polarity. The Doppler velocity asymmetry between the velocity structures of opposite sign reaches its peak values soon after the emergence begins and then gradually drops within 7?–?12 hours. The peak values of asymmetry for the mean and maximal Doppler velocities reach 240?–?460 m?s^?1 and 710?–?940 m?s^?1, respectively. An interpretation of the observable flow of photospheric plasma is given.     

Large-Scale Transport of Magnetic Flux on the sun

The structure of the large-scale background magnetic field evolves in time and space. The large-scale horizontal transport velocity field of the magnetic flux patterns was inferred over the whole solar photosphere in the course of two solar activity cycles from year 1976 to 1999. The method of velocity determination and the testing procedures of the velocity accuracy are presented. The non-axially symmetric component of the horizontal velocity was found and both zonal and meridional velocity regions were described. The horizontal large-scale transport velocity regions vary in shape and the intensity during different phases of the 11-year solar activity cycle. The total horizontal transport velocity is characterized by the presence of variable amounts of the vector field vortices with symmetric orientation relative to the solar equator. The zonal velocity regions, distributed inside of the zonal belt limited by latitudes ± 35°, are persistent for about 4 Carrington rotations. Recurrent structures of similar velocity distributions are not coherent over the whole solar photosphere.     

Magnetic field effect on the fine structure of convective motions in the solar atmosphere

Statistical properties of solar granulation in an active region on the solar surface from the photosphere to the lower chromosphere are studied. We use the values of the velocity, intensity, and magnetic field that were obtained at different heights in the solar atmosphere according to the observation data on the VTT telescope at Observatorio del Teide, Tenerife. The changes in the line??s parameters (central depth of the line, halfwidth, equivalent width, and central depth shift) and convective velocity are presented as functions of the value of the magnetic field. We propose a 16-column model of solar granulation depending on the direction of motion of convective elements and on the sign of contrast at two heights??in the continuous spectrum and in the highest layer (h = 650 km). We found that the magnetic field impedes the change in the sign and motion direction of convective elements.     

Discrete cellular scales of solar convection

The theoretical power spectrum of velocity fields and flux fluctuations at the solar photosphere is calculated using a quasi-nonlinear framework of superposition of unstable convective eigenmodes excited in the solar convection zone. It is demonstrated that this power spectrum exhibits at least three distinct peaks corresponding to granulation, mesogranulation and supergranulation. The vertical velocity and the brightness fluctuation at the solar surface are found to be correlated. The theoretical framework can be adopted for application to other types of stars in order to predict the dominant length scales in the power spectrum of convection in these stars.     

Physical properties of the quiet solar chromosphere–corona transition region

The physical properties of the quiet solar chromosphere–corona transition region are studied. Here the structure of the solar atmosphere is governed by the interaction of magnetic fields above the photosphere. Magnetic fields are concentrated into thin tubes inside which the field strength is great. We have studied how the plasma temperature, density, and velocity distributions change along a magnetic tube with one end in the chromosphere and the other one in the corona, depend on the plasma velocity at the chromospheric boundary of the transition region. Two limiting cases are considered: horizontally and vertically oriented magnetic tubes. For various plasma densities we have determined the ranges of plasma velocities at the chromospheric boundary of the transition region for which no shock waves arise in the transition region. The downward plasma flows at the base of the transition region are shown to be most favorable for the excitation of shock waves in it. For all the considered variants of the transition region we show that the thermal energy transfer along magnetic tubes can be well described in the approximation of classical collisional electron heat conduction up to very high velocities at its base. The calculated extreme ultraviolet (EUV) emission agrees well with the present-day space observations of the Sun.     

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earth's orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).     

The influence of a photospheric spectrum of turbulence on the profiles of weak Fraunhofer lines

We assume that the motion field in the solar photosphere is described by a spectrum of turbulence, defined by suitably chosen parameters. For various values of the spectral parameters we compute average (i.e. averaged over a sufficiently large part of the photosphere) profiles of weak Fraunhofer lines. The resulting profiles which represent the distribution function of line-of-sight velocity components as modified by the transfer of radiation through the atmosphere, are thereupon still broadened by a function representing the influence of the distribution function of the granulation cell sizes. The resulting functions should be compared with the distribution function of line-of-sight velocity components as derived from observations, in order to arrive at an observational derivation of the parameters of the photospheric spectrum of turbulence.     

Comparisons of Supergranule Characteristics During the Solar Minima of Cycles 22/23 and 23/24

Supergranulation is a component of solar convection that manifests itself on the photosphere as a cellular network of around 35 Mm across, with a turnover lifetime of 1 – 2 days. It is strongly linked to the structure of the magnetic field. The horizontal, divergent flows within supergranule cells carry local field lines to the cell boundaries, while the rotational properties of supergranule upflows may contribute to the restoration of the poloidal field as part of the dynamo mechanism, which controls the solar cycle. The solar minimum at the transition from cycle 23 to 24 was notable for its low level of activity and its extended length. It is of interest to study whether the convective phenomena that influence the solar magnetic field during this time differed in character from periods of previous minima. This study investigates three characteristics (velocity components, sizes and lifetimes) of solar supergranulation. Comparisons of these characteristics are made between the minima of cycles 22/23 and 23/24 using MDI Doppler data from 1996 and 2008, respectively. It is found that whereas the lifetimes are equal during both epochs (around 18 h), the sizes are larger in 1996 (35.9 ± 0.3 Mm) than in 2008 (35.0 ± 0.3 Mm), while the dominant horizontal velocity flows are weaker (139 ± 1 m s⁻¹ in 1996; 141 ± 1 m s⁻¹ in 2008). Although numerical differences are seen, they are not conclusive proof of the most recent minimum being inherently unusual.     

On the sun's pole-equator flux differences

We study the possibility that large flux differences between the poles and the equator at the bottom of the solar convective zone are compatible with the small differences observed at the surface. The consequences of increasing the depth of the convective zone due to overshooting are explored.A Boussinesq model is used for the convective zone and we assume that the interaction of the global convection with rotation is modelled through a convective flux coefficient whose perturbed part is proportional to the local Taylor number. The numerical integration of the equations of motion and energy shows that coexistence between large pole-equator flux differences at the bottom and small ones at the surface is possible if the solar convective zone extends to a depth of 0.4R . The angular velocity distribution inside the convective zone is in agreement with the -dynamo theories of the solar cycle.     

Response of an optically thin,isothermal atmosphere to a convective overshoot

Radiation is believed to be hostile to the generation of gravity waves by granulation at the base of photosphere where the radiation is effective. A convective overshoot from subphotosphere seems able to penetrate to a height where the solar temperature is minimum and to excite the gravity waves in a stable region there.The response of the solar atmosphere to a Gaussian disturbance characterizing such a convective overshoot is studied in an unbounded isothermal atmosphere. Radiative effects are included, but only in regions which are optically thin. The response is measured in terms of mean vertical kinetic energy density (E _z) and mean vertical external energy flux (Q _z). E _z and Q _z were calculated for a wide range of frequencies centered at the observed 5-min velocity oscillation period. The computed sharp and broad power spectra at the lower chromosphere and the upper photosphere, respectively, are attributed to the combined effects of space damping and source function. Low-frequency waves (2000 s or longer) are found to be not responsible for depositing energy in the upper solar atmosphere.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the applicability of Goldberg and Unno's method to the determination of microturbulent velocities in an atmosphere with convection

The method of Goldberg and Unno for the determination of microturbulent velocities in a stellar atmosphere is only applicable if there are no macroturbulent or convective motions.If such motions occur, as in the solar photosphere, the derived results are false and may lead to misinterpretations such as an increase of the microturbulent velocity with depth or anisotropic microturbulence.     

Radial velocity field in the lower atmosphere of the solar active region during a flare with an ejection: The initial phase of the flare

Horizontal motion has been studied of the matter along the active region at different heights of the photosphere (115–580 km) in the initial phase of the two-ribbon solar flare on September 4, 1990, near the solar limb, accompanied by the ejection. Photospheric velocities varied in the range −3.5 ... 2.5 km/s. The direction of motion in the photosphere and the chromosphere was mainly toward the observer. Kinematic elements have been discovered in the structure of the horizontal velocity field. Their size reduced as they approached the maximum of the flare from 7–12 to 4–5 Mm, and the velocity amplitude decreased. Throughout the whole investigated active region, vortex motions were observed in the photosphere and chromosphere. Temporal changes in the horizontal velocity field in node areas and in their vicinity were oscillatory in nature and occurred almost simultaneously along the entire height of the photosphere.     

Simulations of magnetic-flux transport in solar active regions

We simulate the evolution of several observed solar active regions by solving a transport equation for magnetic flux at the photosphere. The rates of rotation, meridional flow, and diffusion of the flux are determined self-consistently in the calculations. Our findings are in good quantitative agreement with previous measures of the rotation rate and diffusion constant associated with photospheric magnetic fields. Although our meridional velocities are consistent in direction and magnitude with recently reported poleward flows, relatively large uncertainties in our velocity determinations make this result inconclusive.Laboratory for Computational Physics.E. O. Hulburt Center for Space Research.     

Observations of very low-contrast white-light solar structures utilizing differential photometry

The spatial derivative of the intensity structure of the photosphere has been investigated utilizing a differential photometer system capable of recording intensity variations on the solar disc of 0.05% per arc sec. Time evolution images of the differential intensity profile for a 562.5 arc sec segment of the solar photosphere show a high degree of structure. To a large extent the observed structure persists for times greater than one hour and is rather highly ordered in spatial distribution. Power spectra of the spatial structure averaged over one hour show maxima at 28000 km and 16000 km, close to the spatial scale expected for intensity perturbations from supergranulation.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Magnetic reconnection in the temperature minimum region and prominence formation

Magnetic reconnection at the photospheric boundary is an essential part of some theories for prominence formation. We consider a simple model for reconnection in this region. Parameters of the reconnecting current sheet are expressed in terms of the concentration and temperature of the outside dense and cold plasma, magnetic field intensity, and velocity of convective flows at the photosphere. The reconnection process is shown to be most efficient in a layer several hundred kilometers thick coinciding with the temperature minimum region of the solar atmosphere. The calculated upward flux of matter through the current sheet ( 10¹¹–10¹² g s^–1) is amply sufficient for prominence formation in the upper chromosphere or lower corona.     

Photosphere model of 2N/2M solar flare: July 18, 2000

We investigate the photosphere parameters of a 2N/M2 solar flare that occurred in the NOAA 9077 active area on 18 July, 2000 before its maximum. We use Echelle Zeeman spectrograms obtained in orthogonal circular polarizations by means of a solar spectrograph of the astronomical observatory of Kiev National University, Ukraine (Kurochka, E.V., et. al, 1980). The photosphere is simulated by SIR software (Ruiz Cobo, B. and del Toro Inesta, J.C., 1992). The model of the flare??s photosphere is characterized by a two-component structure, including a magnetic flux tube and its nonmagnetic environment. For both components, we obtain the height distribution of the following parameters: temperature, magnetic field density and line-of-sight velocity. The temperature in the magnetic flux tube increases to approximately 5100 K in the upper photosphere layer of 250?C400 km. The magnetic field intensity decreases sharply from 2600 G (lower photosphere) to 100 G (middle photosphere) with a gradient of about 12 G/km. The model of the nonmagnetic environment differs slightly from the model of undisturbed photosphere.